In this paper we introduce and study a model for electrical activity of cardiac membrane which incorporates only an inward and an outward current. This model is useful for three reasons: (1) Its simplicity, comparable to the FitzHugh-Nagumo model, makes it useful in numerical simulations, especially in two or three spatial dimensions where numerical efficiency is so important. (2) It can be understood analytically without recourse to numerical simulations. This allows us to determine rather completely how the parameters in the model affect its behavior which in turn provides insight into the effects of the many parameters in more realistic models. (3) It naturally gives rise to a one-dimensional map which specifies the action potential duration as a function of the previous diastolic interval. For certain parameter values, this map exhibits a new phenomenon-subcritical alternansthat does not occur for the commonly used exponential map.

Background Human gene variants affecting ion channel biophysical activity and/or membrane localization are linked with potentially fatal cardiac arrhythmias. However, the mechanism for many human arrhythmia variants remains undefined despite over a decade of investigation. Post-translational modulation of membrane proteins is essential for normal cardiac function. Importantly, aberrant myocyte signaling has been linked to defects in cardiac ion channel post-translational modifications and disease. We recently identified a novel pathway for post-translational regulation of the primary cardiac voltage-gated Na+ channel (Nav1.5) by CaMKII. However, a role for this pathway in cardiac disease has not been evaluated. Methods and Results We evaluated the role of CaMKII-dependent phosphorylation in human genetic and acquired disease. We report an unexpected link between a short motif in the Nav1.5 DI-DII loop, recently shown to be critical for CaMKII-dependent phosphorylation, and Nav1.5 function in monogenic arrhythmia and common heart disease. Experiments in heterologous cells and primary ventricular cardiomyocytes demonstrate that human arrhythmia susceptibility variants (A572D and Q573E) alter CaMKII-dependent regulation of Nav1.5 resulting in abnormal channel activity and cell excitability. In silico analysis reveals that these variants functionally mimic the phosphorylated channel resulting in increased susceptibility to arrhythmia-triggering afterdepolarizations. Finally, we report that this same motif is aberrantly regulated in a large animal model of acquired heart disease and in failing human myocardium. Conclusions We identify the mechanism for two human arrhythmia variants that affect Nav1.5 channel activity through direct effects on channel post-translational modification. We propose that the CaMKII phosphorylation motif in the Nav1.5 DI-DII cytoplasmic loop is a critical nodal point for pro-arrhythmic changes to Nav1.5 in congenital and acquired cardiac disease.

The Fenton-Karma model is a simplification of complex ionic models of cardiac membrane that reproduces quantitatively many of the characteristics of heart cells; its behavior is simple enough to be understood analytically. In this paper, a map is derived that approximates the response of the Fenton-Karma model to stimulation in zero spatial dimensions. This map contains some amount of memory, describing the action potential duration as a function of the previous diastolic interval and the previous action potential duration. Results obtained from iteration of the map and numerical simulations of the Fenton-Karma model are in good agreement. In particular, the iterated map admits different types of solutions corresponding to various dynamical behavior of the cardiac cell, such as 1:1 and 2:1 patterns. (c) 2002 American Institute of Physics.

Ankyrin-B is a multifunctional adapter protein responsible for localization and stabilization of select ion channels, transporters, and signaling molecules in excitable cells including cardiomyocytes. Ankyrin-B dysfunction has been linked with highly penetrant sinoatrial node (SAN) dysfunction and increased susceptibility to atrial fibrillation. While previous studies have identified a role for abnormal ion homeostasis in ventricular arrhythmias, the molecular mechanisms responsible for atrial arrhythmias and SAN dysfunction in human patients with ankyrin-B syndrome are unclear. Here, we develop a computational model of ankyrin-B dysfunction in atrial and SAN cells and tissue to determine the mechanism for increased susceptibility to atrial fibrillation and SAN dysfunction in human patients with ankyrin-B syndrome. Our simulations predict that defective membrane targeting of the voltage-gated L-type Ca(2+) channel Cav1.3 leads to action potential shortening that reduces the critical atrial tissue mass needed to sustain reentrant activation. In parallel, increased fibrosis results in conduction slowing that further increases the susceptibility to sustained reentry in the setting of ankyrin-B dysfunction. In SAN cells, loss of Cav1.3 slows spontaneous pacemaking activity, whereas defects in Na(+)/Ca(2+) exchanger and Na(+)/K(+) ATPase increase variability in SAN cell firing. Finally, simulations of the intact SAN reveal a shift in primary pacemaker site, SAN exit block, and even SAN failure in ankyrin-B-deficient tissue. These studies identify the mechanism for increased susceptibility to atrial fibrillation and SAN dysfunction in human disease. Importantly, ankyrin-B dysfunction involves changes at both the cell and tissue levels that favor the common manifestation of atrial arrhythmias and SAN dysfunction.

Normal cardiac excitability depends on the coordinated activity of specific ion channels and transporters within specialized domains at the plasma membrane and sarcoplasmic reticulum. Ion channel dysfunction due to congenital or acquired defects has been linked to human cardiac arrhythmia. More recently, defects in ion channel-associated proteins have been associated with arrhythmia. Ankyrin-B is a multifunctional adapter protein responsible for targeting select ion channels, transporters, cytoskeletal proteins, and signaling molecules in excitable cells, including neurons, pancreatic β-cells, and cardiomyocytes. Ankyrin-B dysfunction has been linked to cardiac arrhythmia in human patients and ankyrin-B heterozygous (ankyrin-B(+/-)) mice with a phenotype characterized by sinus node dysfunction, susceptibility to ventricular arrhythmias, and sudden death ("ankyrin-B syndrome"). At the cellular level, ankyrin-B(+/-) cells have defects in the expression and membrane localization of the Na(+)/Ca(2+) exchanger and Na(+)-K(+)-ATPase, Ca(2+) overload, and frequent afterdepolarizations, which likely serve as triggers for lethal cardiac arrhythmias. Despite knowledge gathered from mouse models and human patients, the molecular mechanism responsible for cardiac arrhythmias in the setting of ankyrin-B dysfunction remains unclear. Here, we use mathematical modeling to provide new insights into the cellular pathways responsible for Ca(2+) overload and afterdepolarizations in ankyrin-B(+/-) cells. We show that the Na(+)/Ca(2+) exchanger and Na(+)-K(+)-ATPase play related, yet distinct, roles in intracellular Ca(2+) accumulation, sarcoplasmic reticulum Ca(2+) overload, and afterdepolarization generation in ankyrin-B(+/-) cells. These findings provide important insights into the molecular mechanisms underlying a human disease and are relevant for acquired human arrhythmia, where ankyrin-B dysfunction has recently been identified.